First Year Progress Report 2010 (Yuan)

8/10/2019 First Year Progress Report 2010 (Yuan)

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Waves and Oscillations in the SolarCorona

First Year Progress Report

Ding Yuan

Supervisor: Professor Valery Nakariakov

April 15, 2010

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Abstract

A progress report is summaried about the research background andon-going project after 6 months work. Our research on MHD wavesand oscillation in the solar corona is covered in general format, headedwith the motivation on the research and main challenges in the field asSection 1, a specialized subsection is delivered to modern instruments(Section 1.1), which are used in the research. This is followed by ainstroduction to solar corona (Section 2), with the main objects thatwilll be encountered in the context almost in any solar research andpublication. Then, the plasma theory about the waves and oscillations(Section 3) is given in general formulary, which is the basic and thetheoretical source to explain other wave related issues in the astro orfusion plasma. A more specified cylinderial model based on the wave

theory (Section 4) is briefed and leads to the theory of propagatingslow-mode MHD waves and its observations and research methodology(Section5). Current project (Section 6) is summaried including thepreliminary results, finally the future plan (Section7) is proposed tillthe Dec 2010. The five key texts are reviewed and added as appendice.

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Contents

1 Motivation 41.1 Modern Instruments . . . . . . . . . . . . . . . . . . . . . . . 4

2 Solar Corona 52.1 Active Region . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Coronal Loops . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Solar Plume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.4 Prominence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Waves and Oscillations in the Plasma 6

4 Standard Model: Straght Plasma Cylinder 8

5 Propagatingclearly Perturbation of Intensity 9

6 Current Projects 11

7 Future Plan 157.1 Shot Term Plan: April - June 2010 . . . . . . . . . . . . . . . 157.2 Long Term Plan: July - December 2010 . . . . . . . . . . . . 157.3 Year 2 and 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Appendices 19

A Nakariakov and Verwichte (2005) 19

B De Moortel (2009) 20

C Torrence and Compo (1998) 21

D Scargle (1982) 22

E DeForest and Gurman (1998) 22

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nal Explorer (TRACE), Solar TErrestrial RElation Observatory (STEREO)

/Extreme UltraViolet Imager (EUVI), Solar Dynamiv Observatory (SDO)/Atmospheric Imaging Assembly

TRACE is a small satellite explorer program to investigate the dynamicsof the magnetized plasma at the transitional region and corona with hightemporal and spatial resolution. In the optics, the visible light is excludedfrom by three thin film aluminium filters, the primary and secondary mirrorsare coated and optimized for one of the EUV wavelengthes, after passingthe mirrors, the EUV light hits the fluorescent lumogen coating of the CCDcamera. The 1k1k CCD detector collects images over an 8.58.5 field ofview (FOV), filtered by one of the four normal-incidence coatings optimizedfor EUV and UV lights, e.g. 171A (FeIX),195A (FeXII), 1600A(W L) etc.

The resolution is 0.5

per pixel, the cadence time can be short as 10s.EUVI is one of the five-telescope package, The Sun Earth Connection

Coronal and Heliospheric Investigation (SECCHI), in the STEREO mission.It images the solar chromosphere and low corona out to 1.7R in four narrowEUV bands: 171A (FeIX), 195A (FeXII) etc. The EUV radiation is filteredat the entrance aperture by a thin aluminium filter of width 150nm, whichsuppresses most of UV,visible and IR radiation and screen out solar heat.Then the emissions are further selected by one of the four quadrant of theoptics, the primary and secondary mirrors are coated with a narrow-band,multilayer reflective coating, optimized for one of the EUV lines. Redundantthin-film aluminium filters are placed in the optic pathway to further remove

the visible and IR radiation, before the backside illuminated CCD collectsthe radiation and produce a image of size 2k 2k of spatial scale of 1.6pixels.

SDO is launched recently under NASAs program: Living With the Star,to better understand the solar variabilities at small temporal and spatialscale. AIA is designed for unprecedented understanding the solar coronaat the around 1.3R, at multiple wavelength simultaneously, the outputimages will cover the whole disk of the sun with the size of 4k 4k at aresolution of 0.5 arc sec and cadence time of 10 sec or better. There are fourtelescopes providing 7 channels of EUV and UV lights, 4 of which provideunexplored temperature view of the sum, and 6 of which observe the ionized

iron at a narrow band and cover the temperature range form 1MK to 20MK.

2 Solar Corona

Corona is also known as the upper atmosphere of the sun. According tothe light sources, it is categorized into three type: K-corona, F-corona andE-corona. K-corona (kontinuierlich, German continuous) consists of contin-uous spectra from the scattering of free electrons, Doppler broadening ofreflected absorption lines from photosphere; F-corona, Fraunhofer scatter-

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ing from the dust particles; E-corona, emission lines from the corona. The

corona exhibits plenty of phenomena, e.g. active region,coronal loops, solarplume, prominence etc.

2.1 Active Region

Active region is a strongly magnetized region of the sun, where the fieldlines extended from the photosphere into the chromosphere and corona,where the sunspots, usually occurs. Active regions emit strong X-rays andUV radiations in association of solar flares and coronal mass ejections. Theactive region are allocated numbers in form of AR+ four digits, by theNational Oceanic and Atmospheric Administration (NOAA) of USA.

2.2 Coronal Loops

Coronal loops are well known structures of the lower corona and transitionregion of the Sun. They mainly emerge from chromosphere, updirected fromthe sunspots, and end up at foot point of opposite magnetic polarization.The coronal loops are closed magnetic flux filled with hot plasma, the plasma is relatively small, at 0.1 or less. These plasma tube structures are verygood media for the wave and oscillationary activities, e.g. sausage mode,kink mode, propagating waves, Alfven waves etc.

2.3 Solar Plume

Solar plumes are long, feathery structures extending into the space from thepoles of the sun. There are hot high-speed streams of plasma erupted fromthe solar plumes. Propagating compressive waves are observed in the solarplume (Deforest and Gurman [1998]).

2.4 Prominence

Prominence is a cool dense plasma structure off the solar limb, suspendingfrom the solar surface.The temperature is much lower than the corona, Theprominence extend outward in the ambient corona in large scale over time

scale of several days or even months. Some of the prominences break apartand induce corona mass ejections. When the prominences are observed inthe solar disk, they are called solar filaments.

3 Waves and Oscillations in the Plasma

Plasma waves and oscillations are well described by the MHD theory andare implemented in various field, e.g. plasma diagnostics, plasma heatingetc. The dispersion relation for the waves is derived by introducing a per-turbation of the physical parameters in equilibrium.

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The ideal MHD equations include continuity equation,the momentum

equation, the energy equation (adiabatic for ideal MHD), Maxwells equa-tions and Ohms law (Derivations follow the context in Aschwanden [2005]),

D

Dt+v= 0 (1)

Dv

Dt = p g+ j B (2)

D

Dt(p) = 0 (3)

B = 0j (4)

E=

B

t (5)

B = 0 (6)E= v B (7)

(8)

The MHD equations are rewriten by introducing the sound speedc2s =p/,and p= c2s , the parameters are reduced to,v, and B

D

Dt+v= 0 (9)

Dv

Dt

=

c2s

g+

1

0[

1

2B2 + ( B

) B] (10)

B

t = B( v) + ( B )v (v ) B (11)

Considering the first order perturbations of each quantity:

(x, t) =0+1(x, t)

v(x, t) =v1(x, t)

B(x, t) = B0+ B1(x, t)

Assume that homogeneous magnetic field is only in z-direction, B0= (0, 0, B0),the associated Alfven speedvA= B0/00, and neglecting the large scalegravitational term (0g). Combining these equations into,

4 vt4

(c2s+v2A)2

t22 v+c2sv2A

2

z22 v= 0 (12)

In order to obtain the dispersion relation, the perturbations is expressed inFourier components, in form of harmonic spatio-temporal function, exp[i(kxt)], For the fast and slow magnetic-acoustic waves

4 k2((c2s+v2A))2 +k2zk2c2sv2A = 0 (13)

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The solutions are much dependent on the initial condition, the relative mag-

nitude of sound and Alfven speed, According the phase speed of the solu-tions, the waves are referred as fast mode wave for larger phase speed andslow mode waves for small ones. Another important factor strongly influ-encing the solutions is the plasma structures: plasma slab, plasma cylinderetc. There are good models for solar feature, the plasma cylinder is a verygood model of corona loops, which will be covered in the following section.

4 Standard Model: Straght Plasma Cylinder

The magnetic cylinder is believed to model well the coronal loops, and ex-tended in geometry to suit the filaments and solar plumes. The standard

model is a simple straight cylinder of plasma, of which the internal and ex-ternal parameters are different, but of cylindrical symmetry. The interior isfilled with plasma of density 0, pressure p0 in a magnetic field ofB0z. Theassociated sound speed, Alfven speed and tube speed are defined respectivelyas C2s0= p0/0, C

2A0= B

20/(0/0), C

2T0= C

2s0C

2A0/(C

2s0+ C

2A0), while the

exterior is the ambient plasma of density density e, pressure pe in a mag-netic field ofBez. The corresponding sound speed, Alfven speed and tubespeed areC2se= pe/e,C

2Ae= B

2e/(0/e) andC

2Te = C

2seC

2Ae/(C

2se + C

2Ae).

The boundary condition requires to balance the total pressure or the dis-placement.

p0+

B2020 =pe+

B2e2e r0= re (14)

The derivation of the dispersion relation is based on linearisation of theMHD equations and the first order differential equation, perturbed at equi-librium condition with aPtot(r)exp[i(kzz +mt)], (Sakurai et al. [1991],Nakariakov and Verwichte [2005])

Dd

dr(rr) = (C

2s +C

2A)(

2 C2TK2z )(2 +m2

r2)rPtot (15)

d

dr(Ptot) =0(

2 C2Ak2z)r (16)

im

r

Ptot= 0(2

C2Ak

2z) (17)

where the r and are perturbations displacement in the radial and az-imuthal directions. The parameters D and are defined as

D= 0(C2s +C

2A)(

2 C2Ak2z)(2 C2Tk2z) (18)2() = (

2 C2sk2z)(2 C2Ak2z)(C2s +C

2A)(

2 C2Tk2z) (19)

The second and third equations can be rewritten as

(2 C2Ak2z)[d2

dr2+

1

r

d

dr (2+

m2

r2)]Ptot = 0 (20)

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adiabatic index, = T5/2 is the thermal conductivity along the magnetic

field,0 is the compressive viscosity coefficient, andg(s) is the gravitationalacceleration along the loop coordinate s,

g(s) =g cos(s

r)(1 +

r

R sin(sr ))2.

The above equations lead to modified Burgers equation, which can be solvedby introducing Fourier components,

v

s v

2n+

+ 1

2csv

v

R0(0)

20(s)

2v

2 = 0 (25)

v(s) =v(0) exp[ s0 (

1

2n(x) ) R

0(0)k

2

20(x) dx] (26)

where = s cst is the comoving coordinate in the sound speed frame,n(s) = c

2s/(g) is the local density scale height, k = /cs is the wave

number, and is defined as

= 1

0(0)csR[40

3 +

( 1)2Rgas

].

The slow-mode MHD waves were observed a lot in multiple wavelenghswith various instruments (see Table-1). The typical speed are measuredlower than the acoustic speed at coresponding temperature, as measure-ments were subjected to the projection effect along the line of sight. Themethod to detect the signal of propagating intensities is proposed in De-forest and Gurman [1998]. The EUV emission flux profile F(s, t) along theloops is first extracted from the images or datatube, normally, the integralaverage should be taken to suppress the random noise, either constant pixelswide along the loop structures or the average of the cross-sections withinthe diffuse coronal structures. Then contour image ofF(s, t) is ploted withs and t as axises, this is called a time-distance plot, in which the ripplepatterns are visible. With time-distance plot, the maximum of the intensityenvelop at each location s is measured, a linear fitting of the peaks will givethe propagating speed of the wave (Fig.1, King et al. [2003]). King et al.[2003] reported a two wavelenghs study (171A and 195A) of propagatingslow wave, the measured periods by wavelet method and estimated speedsare reported to be 23 mins and 58 mins, and 150190km/s, respectively,while the mean sound speeds are, for 171A, cs 147km/s at T 1.0MK,for 195A, cs 180km/s at T 1.5MK. These results are well consistantwith the theory. There is another way to visualized the propagating featureclearly, by ploting the running diffrence plot, namelyF(s, t) F(s, tt),in which case the diagnoal ridges are clearly indentified, the measurement ofthe slopes will give the propagating speed (Fig.2, De Moortel et al. [2000]).

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The estimated period and speed are 180 420 seconds and 70 165km/s(see Table-1).

The obervations of polar plumes were reported by Deforest and Gurman[1998], which is summarized in the appendice. The recent advances, includ-ing the the link with other studies in chromosphere and transition region,were reviewed by De Moortel [2009], also summarized in the appendice.

Table 1: Overview of slow MHD waves observated in coronal structures,N is the number of event, adapted from Aschwanden, Physics of the SolarCorona, chapter 8, p.334 and De Moortel 2009

Observer N Wavelength(s) Speed v [(km/s)] Instrument

DeForest & Gurman (1998) 1 171A 75 150 SoHO/EITBerghmans & Clette (1999) 3 195A 75 200 SoHO/EIT

Nightingale et al.(1999) 1 171A, 195A 130 190 TRACESchrijver et al.(1999) 1 195A 70 100 TRACEDe Moortel et al.(2000) 1 171A 70 165 TRACEDe Moortel et al.(2002a) 38 171A 122 43 TRACEDe Moortel et al.(2002b) 4 195A 150 25 TRACERobbrecht et al.(2001) 4 171A,195A 65 150 EIT, TRACEBerghmans et al.(2001) 1 171A,195A EIT, TRACESakurai et al.(2002) 1 5303A 100 NorikuraKing et al.(2003) 1 171A, 195A 150 190 TRACEMarsh et al.(2003) 1 171A, 368A 50 195 CDS, TRACEMcEwan & De Moortel (2006) 25 171A 98 6 TRACE

6 Current Projects

My currently project is to study the slow-mode propagating MHD waves,focusing on the spatial variation and correlations and long period behaviors,especially the 3mins oscillation. The images of size 512 512 are taken byTRACE in two bandpasses 171A and 195A. The whole observation programlasts for around 5days, from 31 - Jun - 1998 UT 00:00.000 to 04 - Jul - 1998UT 23:59.999, the data are mostly continuous observations, except someroutine pointing to the solar limb for about half a hour to one hours. Verygood propagating waves are clearly seen by eye.

The dataset from TRACE in FITS file are first prepared by using the IDLroutine in SolarSoft, TRACE PREP, calibrations are done by implementa-tion of this procdure, optional key word are added: /wave2point corret, theimages pointings are aligned to the reference wavelength, which are assuredto be correct; /unspike, /destreak: the spike and streaks from radiation beltand cosmic ray are removed; /deripple will remove the readout noise of the

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Figure 1: Top left panel: active region AR8253, imaged by TRACE on 2 July1998 UT 06:00 in the 195A bandpass. Top right panel: the slits analysed,where apparen propagating intensities are observed. Bottom panel: Thetime-distance plot of along slit A marked in the top-right panel, the time-distance plots of both bandpass 171A and 195A are placed in parallel, butopposite direction. King et al. [2003]

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Figure 2: Top panel: the active region AR8496, observed by TRACE 171Aat 24-Mar-1999 UT 06:47, subimage on the top-right is the area supportingthe propagating intensities. Bottom panel: the running diffrence of theregion indicated on the top image, the positions are pixel index, rather thanthe real position, a clear ridge is visible, the periods and propagating speedare measured to be 180 420 seconds and approximately 70 175km/s,respectively. De Moortel et al. [2000]13


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CCD, /normalize keyword will normalize the output image to the exposure

time into DN per second, as the exposure times are subjected to slight vari-ation, and the CCD response signals are found to be linear proportionalto the exposure time; /float will give the output images in float value foreach pixels, rather than intergers, which will increase the storage size ofthe images, however, this will facillitate further processing to an enhancedpreciseness.

The next step that have been done is to trace the target in the images asprecise as possible. The active regions in the images are in different locationsdue to multiple effect. It is co-rotating with the solar surface, and axis ofthe sun is also gyrating in long period, e.g.days . The spacecraft repointedfrequently to include the target in the image range 8.5

8.5, the spacecraft

is subjected to slight pointing drift, which is negligible for short duration lessthan hours, but is rather severe for long period of observation. The dataset isof size data(nx,ny,nt), wherenx and ny are the numbers of pixels in x andy axis,ntis the time index of the images. For two images with center of view(XCEN(0), Y CEN(0)) and (XCEN(1), Y CEN(1)), the repointing is de-noted asD = (Dx, Dy) = (XCEN(1)XCEN(0), Y CEN(1))Y CEN(0),The solar differential rotations is calculated as R = (Rx, Ry), (NB. Ry= 0is due to the gyrating of the rotating axis), then the sub dataset of sizesubdata(x1 x0+ 1, y1 y0+ 1, nt) is extracted by

subdata = data[(x0Dx+Rx) : (x1Dx+Rx), (y0Dy+Ry) : (y1Dy+Ry), ]

The region of interest is tracked by considering spacecraft re-pointing andsolar rotation, the uncertainties of the solar rotational model and spacecraftpointing drifts are minimized by correlations. The displacements of theimages are coalign with the reference image by shifting an offset calculatedby cross-correlation with the reference image. The sub dataset, after thisstep are ready for further analysis. The images from sub dataset are thendisplayed in the movie co-rotating with the solar surce,Dx pixels away fromthe reference image.

A slit is extracted from the data to form a time-distance plot as in toppanel of Fig.3. Wave patterns are visible in the image. For each pixel, the

intensity are interpolated into a new evenly spaced datacube of the samesize, as Fast Fourier Transform (FFT) requires strict evenness of the timeseries, the original sampling times are subjected to slight variation due tovarious exposure time. After FFT, a filter is apply to the signal in frequencydoman, optionally ideal or gaussian , with the selected frequency near thecentre of the window. Then the time series are sythesized with the averagevalue subtracted, which are illustrated in the bottom of the bottom panel, asshown in Fig.3. Two ideal filters of frequency band [0.005, 0.006]Hz includ-ing 1/180s = 0.0056Hz and [0.003, 0.004]Hz embraing 1/300s = 0.0033Hz areapplies to the time series. The restored time-distance plot are show in Fig.

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3.These two ideal filters are also apply to the movie, pixel by pixel, then

each pixels should oscilate independently with one another with randomphase and amplitude if there is no collected behaviors, however if propagat-ing slow-mode wave exist, the involved pixels are modulated and apparentpropagating intensity can be observed. The resulting movie confirm thispoint, in the movie filtered by 3-min filter, the propagating intensity areclearly visible, while it vanishes after filtered by the ideal 5-min filter.

7 Future Plan

7.1 Shot Term Plan: April - June 2010

From April to the end of June, I will focus on the slow-mode magneto-acoustic waves, to study its long period evolution of the parateters, e.g.sta-bility of the phase, evolution of the period and propagating speed, and otherfeatures. The procedures to analysis the data were already developed, andthe wave patterns are recognized with the time-distance plot, the next stepis to obtain the parameters, with data analysis technique, e.g. periodogram,windowed FFT, wavelet etc. These can be done in a short time, since thedata are already processed at good stage and the procedures are available,either developed within the group or on the website well acknowledged.

The result of current study will have to be abstracted and submitted tothe BUKS 2010 (Belgium, United Kingdow, Spainn) meeting at St Andrews

University at the end of April: Workshop on MHD waves and seismology ofthe solar atmosphere. The formal submission to a referred journal will beexpected at the end of June.

7.2 Long Term Plan: July - December 2010

After the completion of the first project, it is expected that the data fromthe recently launched SDO/AIA is almost available for the solar community.The next project will be much involved with the advanced instrument.

Jun-Oct: After the initial internal test and software development, thedata should be available on the NASA website. The initial task is

to get familarized with the AIA pre-processing software, and to startanalyzing the similar phenomena, e.g.slow mode MHD waves, sunspotevents with the multi-channel telescopes, the main focus will be stillin the active region and magnetic field dynamics. However if there arenew discoveries beyond the current knowledge level, we will focus onthat. In July or August, another data updating meeting will be held,the feedback will somehow help with the project.

Oct-Dec: The second project will be formally concepted, which de-pends on the advances made by SDO/AIA. I alread gain experience

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Figure 3: Top panel: The typical image taken by TRACE in 171A bandpassat 03 - Jul -1998 UT 00:00, the coronal structure is a diffuse corona, theslit analyzed are maked with dots. Bottom panel: The time distance plotsare stacked in parallel, top one from the original dataset and bottom onefiltered in a narraw ideal rectangular window of period embracing 3mins.Clear ripple patterns are seen from both time-distance plots, especially theideally filtered one. As the time duration for plots are around 2 hours, theripples looks like vertical, however, they are the same as in King et al. [2003],if they were plotted in the same time scale.

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from current project and initial familarization with the the AIA soft-

ware. It will take less time to obtain output from the project, theresult are expected for journal submission before Chrismas.

Backup: If due to some reason, SDO/AIA is not available, we willshift to Nobeyama Rodia Observatory, which is not worth to discussin detail at the current stage.

7.3 Year 2 and 3

Since there exists a risk of the availability of SDO/AIA, The longer planis subjected to large uncertainties, it not realistic to make one, after theinitial analysis of the AIA data for reliabilities and possible break events, a

longer plan should be make in Oct 2010, which will be included in the nextprogress report and reseach plan.

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References

M. J. Aschwanden. Physics of the Solar Corona. An Introduction with Prob-lems and Solutions (2nd edition). December 2005.

D. Berghmans and F. Clette. Active region EUV transient brightenings -First Results by EIT of SOHO JOP80. , 186:207229, May 1999.

I. De Moortel. Longitudinal Waves in Coronal Loops. Space Science Reviews,149:6581, December 2009. doi: 10.1007/s11214-009-9526-5.

I. De Moortel, J. Ireland, and R. W. Walsh. Observation of oscillations incoronal loops. , 355:L23L26, March 2000.

I. De Moortel, A. W. Hood, J. Ireland, and R. W. Walsh. Longitudi-nal intensity oscillations in coronal loops observed with TRACE II. Dis-cussion of Measured Parameters. , 209:89108, September 2002a. doi:10.1023/A:1020960505133.

I. De Moortel, J. Ireland, R. W. Walsh, and A. W. Hood. Longitu-dinal intensity oscillations in coronal loops observed with TRACE I.Overview of Measured Parameters. , 209:6188, September 2002b. doi:10.1023/A:1020956421063.

C. E. Deforest and J. B. Gurman. Observation of Quasi-periodic Com-

pressive Waves in Solar Polar Plumes. , 501:L217+, July 1998. doi:10.1086/311460.

D. B. King, V. M. Nakariakov, E. E. Deluca, L. Golub, and K. G. Mc-Clements. Propagating EUV disturbances in the Solar corona: Two-wavelength observations. , 404:L1L4, June 2003. doi: 10.1051/0004-6361:20030763.

V. M. Nakariakov and E. Verwichte. Coronal Waves and Oscillations. LivingReviews in Solar Physics, 2:3+, July 2005.

V. M. Nakariakov, E. Verwichte, D. Berghmans, and E. Robbrecht. Slow

magnetoacoustic waves in coronal loops. , 362:11511157, October 2000.

T. Sakurai, M. Goossens, and J. V. Hollweg. Resonant behaviour of MHDwaves on magnetic flux tubes. I - Connection formulae at the resonantsurfaces. , 133:227245, June 1991. doi: 10.1007/BF00149888.

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Appendices

A Nakariakov and Verwichte (2005)

Waves and oscillations of the solar corona are well observed with moderninstruments and are believed to the promising candidate in explaining thedilemma of corona heating and acceleration of fast solar winds. Combin-ing the observations and MHD wave theory, the physical parameters, e.g.magnetic field, transport coefficients, fine-structure and heating function areestablished, this is called MHD seismology. Corona waves and oscillations,including the newly developed MHD seismology are discussed in this reviewpaper in the series ofLiving Review of Solar Physics.

A plasma structurestraigh cylinder, which is a good model of coronaloops, is introduced and, further, the dispersion relation with linearizationof the MHD equation under harmonic perturbation to the total presurePtot(r)exp[i(kzz+ m t)]. For the modes that are evanescent outsidethe cylinder. The dispersion relation was three groups of solution: Alvenwave, fast and slow mode waves. The waves is further referred to as sausagemodes (m= 0), kink modes (m= 1) and flute or ballooning modes (m > 1)

A typical kink oscillation of coronal loops was observed with TRACEspacecraft in the AR8270 on 14 July 1998 by Nakariakov et al.1999. Byfitting the loop time displacement plot, The period and decay time wasfound atP = 4.3

0.9min and= 14.5

2.7min. Assuming a density ratio

ofe/0= 0.1, the magnetic field strength is estimated

B0=

00CA0

20L

P

0(1 +e/0)

where0is the magnetic permeability constantLis the length of the loop,CA0is the internal sound speed.

Propagating slow waves, moving at the speed of sound, were first ob-served in coronal holes by Ofman et al.(1997) with SOHO/UVCS, and atsolar plume by DeForest and Gurman (1998). As the sound speed is a func-tion of temperature and adiabatic index , the measured speed, subjected

to projection effect, can serve a tool for coronal seismology. The decreasingcorrelation coefficients along the structure suggested that there might be asubstructure of the active region, which cannnot be resolved with current in-struments. Future studies are very promising to investigate more details, 3Dobservations to compensate the projection effects, and higher temporal andspatial resolutions to dig the possible speed variations and finer structures.

The observation of propagating fast waves is limited by current availableinstruments. Since the period and wavelength of fast waves couldnt be wellresolved by the cadence time and resolution of the detectors. Williams etal. (2001,2002) and Katsiyannis (2003) reported the observations of rapidly

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propagating compressive wave trains in the coronal loops with SECIS. The

estimated speed is about 2100km/s with a mean period of 6 s in a quasi-periodic pattern. The measurement of amplititude agreed well with theoreticmodel (Nakariakov et al.(2003)), however, the large uncertainties limitedfurther analyisis. Verwichte et al.reported the direct observation of cleartransverse fast wave and interpreted as fast magnetoacoustic kink wave.The study was performed with TRACE 195A at a hot supra-arcade abovepost-flare loop arcade. The wave periods and wavelengths were estimatedin the range of 90 220s and 20 40Mm respectively. The plasma slabstructure was more suitable than cylindrical model in order to explain theobservations.

Current observations are very much limited by the availibilities of good

instrument. With the launch of SDO, the AIA detector will send by imagesof the whole sun of size 4k 4k with cadence time 3s and resolution of 0.5,which could boost the activities and complement current knowledge of thewaves.

B De Moortel (2009)

This paper is an updated review of propagating intensity disturbances inquiescent coronal loops that are intensively studied recently, a further ex-tension of another two reviews in 2002, which focus more on the detections ofoscillations, measurements of physical paramenter, statistics of the featuredistributions and metheds of data analyisis. While in this one, more effortswere concentrated on physical and interpretions of the damping features,apparent links to other observations and modellings in the chormosphereand transitional regions, possible triggerring mechanism (e.g. globlal solar5-min p-mode oscillations, leakage from inclined magnetic portals) of thepropagating oscillations.

The propagating intensity perturbations are found to be quasi-periodsand persist for 5 cycles in a wave-train sequence at the period of about3 mins above sunspot umbras and around 5 mins at off-sunspot regions.Theoretical modelling indicated that dissipation causes decay of the per-turbation amplititude, while the effects of gravitirional stratification is thereverse. Further modellings were performed by De Moortel et al. (2004)with inclusion of thermal conduction, compressive viscosity and opticallythin radiation, and found the thermal conduction is the main contributor,while the impacts of the latter two is negligible. The modellings was ex-tended by considering area divergence and gravititional stratification, andwas concluded that the combination of thermal conduction and area diver-gence can account for the observed damping.

Recent studies, both theoretical and observational, show that the incli-nation of magnetic field could provide magnetic portals and allow the globlal

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5 min p-modes leak into the corona. At sunspot umbras, the near-vertical

magnetic fields reflects back the 5-min p-modes, thus 3-min perturbationsare dominating, while at plage region (non-sunspot), the inclined magneticfields are not able to cut-off the 5-min p-modes, so the global surface 5-minp-modes can be observed clearly.

Both upward and downward flows are observed with Hinode / XRT andHinode/EIS near the edges of active regions with Doppler shifts techniques.The speeds of the outflows are found up to 100km/s close to local soundspeeds (corrected by projection effections), and behaves similarly to prop-agating intensity, while non study annouces wave pathern along the flows,so it is worhwhile to investigate this link with high spatial and temperalresolutions.

C Torrence and Compo (1998)

This paper submitted by C. Torrence and G.P. Compo, with its code in FOR-TRAN,C,and IDL, is good practical step-by-step guide to wavelet analysis,with the example from the time series of the El Nino Southern Oscillation(ENSO). the Edge effects due to finite time series beared with WindowedFourier Transform are inherited by wavelet transform and are discussed andillustrated in the samples. The selections of wavelet functions are basedon the features of the time series, complex wavelets for oscillations (This isgood selection for analysis of waves and oscillation) and real-valued waveletsfor those containing singular frequencies components. The significance leveland confidence intervals are calculated with both white and red noises. Thetechniques to improve the quality of analysis are given, such filtering , cross-wavelet spectra etc.

This is a very good guide for obtaining oscillation components confidentlyfrom the time series of solar data. The procedures on their website can bemodified slightly and implemented in short time, A very good colourful fig-ures can be produced quickly at publication level. The only flaw is that thecodes are only ready for evenly-spaced time series, normally the solar datumare semi-even in short period and un-even in long observation, namely, theobservations were made almost in the same intervals with slight variationsof exposure time, and were oriented for other observations, or closed formaintenance, or to avoid strong radiation belts to protect the instruments,routinely during the day and year periods. So for short observations (sev-eral minutes to several hours), interpolation of the time series to even timeintervals is well acceptable, while for long time series with data gaps, othertechniques for unevenly-spaced time series must be implemented, such asLomb-Scargle method (which is also one of the key texts reviewed).

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D Scargle (1982)

The periodogram is a commomly used spetral analysis technique to extractperiodic compoment from unevenly spaced data. Other spetral analysistool are not so efficient, e.g. FFT, wavelet, as unevenly spaced data mightgenerate spurious periods equal to time gaps or their harmonics in the FFTor DWT, however periodogram is able to avoid such incapablities, and it isequivalent to least-fit of sinusoids to the data.

In this paper, the reliability and efficiency of periodogram is studied. Amodification of the classic definations (see Eq. below) is made to retain thestaticstic behavior and more suitable for numerical realizations, upon whichmost of the available codes are based. The staticstical analysis is elaborated

with the inclusion of expressions for false alarm rate and detection efficiency.PX() is the distribution probability of frenquency compoment , definedas,

PX() =1

2{ [

jXjcos (tj )]2jcos

2 (tj ) +[

jXjsin (tj )]2jsin

2 (tj ) }

whereXj is a physical observable at time series tj, is defined as

tan(2) =

j

sin2tj

/

j

cos2tj

The codes for periodogram analysis are available in various formats, alsoour own procedures in IDL (Nakariakov). I will use the routines in IDLto analize the time series extracted from the solar EUV emissions or othertime series in the future. The routine has to be improve to provide moreflexibility and clearance.

E DeForest and Gurman (1998)

Slow-mode waves were first observed in the solar polar plume (open fieldstructure, in contrast to closed structure or coronal loops). With the datain 171A bandpass from SOHO/EIT, DeForest and Gurman (1998) found

filamentary substructure, on a scale of 5, oscillating on the time scalesof several minutes in wave trains of 10 15mins periods. The propagatingspeeds were estimated at 75 150kms1. The quasi-periodic perturbationsto the overall intensity of the plumes amounts to 10% 20%. The energyflux carried by the waves was calculated to be 150 400Wm2 by assumingthe waves to be sonic, it is not sufficient to heat the coronal holes, which isabout 1kWm2 (Parker 1991).

Besides the new observations, another contribution of the paper is thata well accepted procedure to prepare the data for analysis, which is a pre-liminary stage for my future work, was established. Besides the normal

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First Year Progress Report 2010 (Yuan)

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Transcript of First Year Progress Report 2010 (Yuan)